Variations in protocols

Whichever term for BHR is used, challenge with a pharmacological agent or with exercise in children, rather than allergen challenge, is usually implied. Subjects are assessed for eligibility, including adequate baseline lung function. Many different provocation agents have been used1; histamine and methacholine now predominate, although a number of others have recently become popular.2The aerosol generated by a nebuliser is inhaled during inspiration or tidal breathing in increasing doubling concentrations until the chosen measure of lung function has fallen by a predetermined amount from its value measured after inhalation of the diluent, the chosen maximum concentration is reached, or the test is stopped for some other reason.

Although specific conductance and other measures were adopted in some early work,1 ,3 ,4 forced expiratory volume in one second (FEV₁) is now almost always used as the measure of lung function because of its greater reproducibility.2 ,5 Peak expiratory flow is used in exercise challenge if measurement of FEV₁ is impracticable.6 Exercise challenge is not considered further here. As challenge has been made with a single “dose” in general, there are more limited options for expression of the response than with challenge with a pharmacological agent.

The use of FEV₁ is virtually the only point on which testing in adults is standardised, variations in eligibility for challenge, the provoking agent, mode of delivery, starting and maximum concentrations, and expression of the response being found in every possible combination. Clinical and community studies tend to differ in eligibility criteria and maximum dose or concentration; termination of the test when a 20% fall in FEV₁ occurs is usual in community studies but greater falls and higher doses may be achieved when justified clinically and ethically.

Dose or concentration

The result of challenge is a dose or concentration response curve. With the tidal breathing method developed for clinical use results are expressed in terms of concentration of drug delivered,7but it is more common with methods recommended for epidemiological studies to calculate the cumulative dose.8 ,9 Juniperet al suggested that methacholine had a small cumulative effect but that the effect of histamine was non-cumulative.10 However, within one study there will be a close relation between cumulative dose and either the final dose or concentration delivered, and this may explain why the issue was not discussed in the 1993 recommendations.2

Shape of the dose-response curve

The term “dose” will be used from now on, but all that follows applies equally if results are expressed in terms of concentration. If FEV₁ is plotted against the log dose of histamine14 or methacholine,15 a sigmoid curve is obtained in non-asthmatic subjects and in some mild asthmatics.14 Curves may differ in the maximal response (plateau), the slope of the steep part of the sigmoid, or in position. However, it is necessary to administer high doses in order to observe the plateau of the curve in non-asthmatics. Woolcock et algave a cumulative dose of up to 122 μmol histamine to laboratory staff,14 refraining from higher doses because of the side effects. The test was terminated in asthmatic subjects when FEV₁ had declined by 60%, maximal response being assumed to be 100%.

Hence, while high doses may occasionally be given to volunteers,16 it is rarely possible to measure the maximal response in clinical studies and never in epidemiological studies in which a high response rate is required. The consequences of this are that at most the mid-curve slope and position of the curve can be estimated, and the majority of subjects will have reached neither a specified fall in FEV₁ nor a plateau.

Expression of the results

Estimation and analysis of PD₂₀

Although originally thought of as a measure of the sensitivity component of BHR, PD₂₀ (or PC₂₀) has become the most used summary of BHR itself. Provided at least a 20% fall in FEV₁ has been observed, the PD₂₀ can be estimated by linear interpolation between the last two points on the dose-response curve. As doubling doses are used, interpolation is usually carried out on the log dose scale, although there is some evidence that FEV₁ is linearly related to dose.23 ,24 When the FEV₁-log dose is sigmoid, the observed part of that curve is approximately exponential.25 ,26 However, the inherent variability of FEV₁ makes the shape of the curve often difficult to observe for an individual subject, and in clinical use the practicality of linear interpolation on the log dose scale outweighs any other consideration.

It is for community studies that other methods have been recommended, when data are necessarily computerised and maximising information is the priority. Curve fitting enables all the information to be used, rather than just the final two points, and has been shown to improve repeatability slightly.25 In order to increase the number of subjects with a measurable PD₂₀, extrapolation by one doubling dose has sometimes been used but is now thought inadvisable.26

Inevitably, whatever maximum dose of histamine or methacholine is permitted, and whether or not extrapolation is used, most studies find that less than 50% of the population achieve a 20% fall in FEV₁. Hence the percentage with PD₂₀ less than an arbitrary cut off point is the most used summary statistic, and logistic regression is the most used method of analysis to identify risk factors for BHR. The percentage summary is simple to understand but has several drawbacks: (1) it wastes the information in the size of PD₂₀ in those with an estimate; (2) it suggests that BHR is a dichotomy whereas the evidence is that the distribution is unimodal27 ,28; and (3) the value depends on the cut off point used which is normally the maximum dose except for reasons of comparability with other studies.29

Methods to overcome the first and second problems depend on assumptions. These are essentially statistical methods for censored data, an observation being “censored” when it is known only to be above a certain limit, in this case the maximum dose.30Either method designed for censored data can be used directly,30 or survival analysis methods can be exploited, in which dose is treated as “time”, reaching a 20% fall in FEV₁ being the equivalent of failure or death in conventional survival analysis.31 Each method requires the assumption of a distribution for PD₂₀. As most subjects have censored data, only the left hand end of the distribution can be observed, and power to detect departure from any distribution is low. Evidence in favour of a log-Normal distribution has been presented28 ,32 and taken as a fact by some authors,33 but a good fit to a Weibull distribution has also been reported.31 Whether data exist that would show any material difference in goodness of fit, whether this would be generalisable, or whether other positively skewed distributions would fit equally well is not known. The log-Normal distribution leads to estimation of the geometric mean PD₂₀ and “fold difference” or “percent change” between comparison groups.33 The results, assuming a Weibull distribution, are expressed in relative percentiles, the ratio of the doses required for a given percentage of individuals to achieve a 20% fall in FEV₁ in different groups.31

Although statistical programs are now readily available for both analyses, the degree of censoring for PD₂₀ far exceeds that which is recommended for such analyses, and other assumptions of the analyses are untestable. These are more crucial than the distribution assumption for the calculation of p values and confidence intervals—namely, homogeneity of variance of the log-Normal distributions or proportionality of hazard functions in survival analysis.

Continuous measures of BHR

While some authors have tried to maximise use of the information in PD₂₀ by the above methods, others have sought alternative measures of BHR that would enable data from all tested subjects in a population study to be included in a standard statistical analysis. As the percentage decline in FEV₁ with cumulative dose is approximately linear over the range of doses permitted, the slope of this line is very highly correlated with PD₂₀ but can be measured in all subjects challenged. O’Connor et al proposed that the slope should be estimated simply by dividing percentage fall from post-saline FEV₁ at the highest dose given by that final dose.34 Thus an estimate is possible for all subjects given at least one dose of histamine or methacholine. Abramson et al proposed the slope estimated using linear regression.35 This least squares slope requires at least two doses to be administered for estimation to be possible, but uses all information.32

These two measures have immediate appeal but need to be used with caution. Firstly, they require transformation in order to satisfy the statistical requirements.32 Secondly, whether a log transformation or a reciprocal transformation is used, a constant must first be added to remove negative values that can occur in subjects with low BHR. Thirdly, the fact that every subject has a value does not guarantee that the summary measure provides information extra to that in PD₂₀. The two-point slope was found to be poorly repeatable in subjects without a measurable PD₂₀ on both occasions.32 Hence, its use is little better than analysing PD₂₀ using censored regression. The least squares slope was found to be reasonably repeatable, but no simple transformation to a Normal distribution was found.32 Its use is equivalent to estimating PD₂₀ by extrapolation beyond the maximum dose using a linear model. Verlato et al found this to give better agreement with observed values than extrapolation from lower doses using an exponential curve on a logarithmic scale, but with some overestimation of PD₂₀, and consequently cautioned against extrapolation.26 It should be noted that, as all data points are used, these slopes do not measure “reactivity” as defined above.

Importance of variations in protocol and expression of results

Within one study the protocol should be uniform. The continuous slope measures or methods for analysis of PD₂₀ that use all the information, either by censored regression or survival analysis methods, will have greater power to detect group differences than logistic regression of the percentage achieving PD₂₀ at some arbitrary dose.28 No other difference in results has been reported. This is not surprising given the very high correlation between least squares slope on the linear scale and PD₂₀. Although the ECRHS slope and PD₂₀ are less highly correlated, these also have given similar results.29 ,37

At the other extreme, if results are to be compared between different studies, any of the variations in protocol may matter, particularly if levels of BHR are to be compared rather than relations of BHR to risk factors. Comparisons of prevalence of BHR between populations have been hampered, in particular, by the differences in provoking agents, variety of cut off points, and age ranges of the subjects.38 There is little alternative to large scale multicentre studies if truly comparative data are to be obtained. An additional problem is that eligibility criteria necessarily entail exclusion of subjects with poor lung function, many of whom may have high BHR, and this will differ between the populations studied. Here there is an advantage of logistic regression of PD₂₀ as a sensitivity analysis of the assumption that all such subjects have PD₂₀ below the cut off point can be carried out easily.37

Relations of BHR to risk factors can be compared qualitatively between studies employing different protocols, but results may appear different because of sample size differences or the limited power of some analyses. Increasingly, there is a desire to combine results from different studies using meta-analysis.39 Although the method was developed for combining randomised controlled trials, it can also be used to provide a quantitative summary of results from several observational studies, as used in relation to passive smoking.40 In the context of BHR, either odds ratios from logistic regression in relation to the risk factor of interest can be combined or differences in means of one of the continuous measures. If heterogeneity between studies is detected this may be due to any of the variations in protocol that occur. Conversely, differences in protocol may obscure true heterogeneity in the effect of interest. While sensitivity analyses may help to differentiate between true and spurious heterogeneity, the variations in protocol are likely to be too great for this to be convincing. An alternative is to use effect size, the difference in means divided by the within group standard deviation. This provides a dimensionless measure, although it does not guarantee comparability. Calculation of effect size requires a continuous outcome—that is, one of the slope measures—or an estimate of standard deviation of log(PD₂₀) from censored regression.

Conclusion

Given the very many variations in protocol, different ethical requirements in different countries, and suitability of methods in different circumstances, it seems unlikely that researchers or clinicians could agree to standardise the measurement of BHR. The variations may be unimportant in clinical use but hamper the progress of epidemiology. Analysis of percentage PD₂₀ below an arbitrary cut off point by logistic regression is misleading, given the unimodal distribution of BHR in the population, lacks power, and is unhelpful for those wishing to combine results using meta-analysis. Least squares slope or ECRHS slope should be used, or analysis of PD₂₀ using censored regression, while recognising that the first and third are essentially the same analysis in different guises, and that each measure has problems which reflect the nature of the data.